63, 64] 



COMPOSITION OF SCREWS. 



217 



Let us first suppose that the axes of the component screws 

 intersect at right angles, and let us take them for axes of X and Y. 

 Let their pitches be 



^ 8 v 



Let E (Fig. 66), the resultant 

 of E x and E yj make an angle a 

 with the X-axis, and let S, 

 the resultant of S x and S y , 

 make an angle /3 with the 

 same axis. Then the central 

 axis is parallel to E, and cuts 

 the ^-axis at a distance from 

 the origin 



The resultant moment along 

 this line is 



Fig. 66. 



We have now 

 Scos8 



21) 



A x ~T~\ * X T~l 



- Jti x = - i cos a, 



2rt 2n 



S P ~~ P 



OZ = p- sin (/3 a) = -^ - sin a cos a, 



= Scos(,3-)=' 



cos 



in 2 a). 



sn 



For the pitch of the resultant screw we obtain 



_ 



2 ye 





22) 



The equations of the central axis are 



y = x tan a, 



23) t 



Inserting the values 



cos a = 

 we have 



smcos a. 



